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环拓扑（影印版）

样章
作者：
Victor M. Buchstaber, Taras E. Panov
定价：
199.00元
ISBN：
978-7-04-059299-3
版面字数：
860.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2023-03-08
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
拓扑学
暂无
  • 前辅文
  • Chapter 1. Geometry and Combinatorics of Polytopes
    • 1.1. Convex polytopes
    • 1.2. Gale duality and Gale diagrams
    • 1.3. Face vectors and Dehn–Sommerville relations
    • 1.4. Characterising the face vectors of polytopes
    • Polytopes: Additional Topics
    • 1.5. Nestohedra and graph-associahedra
    • 1.6. Flagtopes and truncated cubes
    • 1.7. Differential algebra of combinatorial polytopes
    • 1.8. Families of polytopes and differential equations
  • Chapter 2. Combinatorial Structures
    • 2.1. Polyhedral fans
    • 2.2. Simplicial complexes
    • 2.3. Barycentric subdivision and flag complexes
    • 2.4. Alexander duality
    • 2.5. Classes of triangulated spheres
    • 2.6. Triangulated manifolds
    • 2.7. Stellar subdivisions and bistellar moves
    • 2.8. Simplicial posets and simplicial cell complexes
    • 2.9. Cubical complexes
  • Chapter 3. Combinatorial Algebra of Face Rings
    • 3.1. Face rings of simplicial complexes
    • 3.2. Tor-algebras and Betti numbers
    • 3.3. Cohen–Macaulay complexes
    • 3.4. Gorenstein complexes and Dehn–Sommerville relations
    • 3.5. Face rings of simplicial posets
    • Face Rings: Additional Topics
    • 3.6. Cohen–Macaulay simplicial posets
    • 3.7. Gorenstein simplicial posets
    • 3.8. Generalised Dehn–Sommerville relations
  • Chapter 4. Moment-Angle Complexes
    • 4.1. Basic definitions
    • 4.2. Polyhedral products
    • 4.3. Homotopical properties
    • 4.4. Cell decomposition
    • 4.5. Cohomology ring
    • 4.6. Bigraded Betti numbers
    • 4.7. Coordinate subspace arrangements
    • Moment-Angle Complexes: Additional Topics
    • 4.8. Free and almost free torus actions on moment-angle complexes
    • 4.9. Massey products in the cohomology of moment-angle complexes
    • 4.10. Moment-angle complexes from simplicial posets
  • Chapter 5. Toric Varieties and Manifolds
    • 5.1. Classical construction from rational fans
    • 5.2. Projective toric varieties and polytopes
    • 5.3. Cohomology of toric manifolds
    • 5.4. Algebraic quotient construction
    • 5.5. Hamiltonian actions and symplectic reduction
  • Chapter 6. Geometric Structures on Moment-Angle Manifolds
    • 6.1. Intersections of quadrics
    • 6.2. Moment-angle manifolds from polytopes
    • 6.3. Symplectic reduction and moment maps revisited
    • 6.4. Complex structures on intersections of quadrics
    • 6.5. Moment-angle manifolds from simplicial fans
    • 6.6. Complex structures on moment-angle manifolds
    • 6.7. Holomorphic principal bundles and Dolbeault cohomology
    • 6.8. Hamiltonian-minimal Lagrangian submanifolds
  • Chapter 7. Half-Dimensional Torus Actions
    • 7.1. Locally standard actions and manifolds with corners
    • 7.2. Toric manifolds and their quotients
    • 7.3. Quasitoric manifolds
    • 7.4. Locally standard T-manifolds and torus manifolds
    • 7.5. Topological toric manifolds
    • 7.6. Relationship between different classes of T-manifolds
    • 7.7. Bounded flag manifolds
    • 7.8. Bott towers
    • 7.9. Weight graphs
  • Chapter 8. Homotopy Theory of Polyhedral Products
    • 8.1. Rational homotopy theory of polyhedral products
    • 8.2. Wedges of spheres and connected sums of sphere products
    • 8.3. Stable decompositions of polyhedral products
    • 8.4. Loop spaces, Whitehead and Samelson products
    • 8.5. The case of flag complexes
  • Chapter 9. Torus Actions and Complex Cobordism
    • 9.1. Toric and quasitoric representatives in complex bordism classes
    • 9.2. The universal toric genus
    • 9.3. Equivariant genera, rigidity and fibre multiplicativity
    • 9.4. Isolated fixed points: localisation formulae
    • 9.5. Quasitoric manifolds and genera
    • 9.6. Genera for homogeneous spaces of compact Lie groups
    • 9.7. Rigid genera and functional equations
  • Appendix A. Commutative and Homological Algebra
    • A.1. Algebras and modules
    • A.2. Homological theory of graded rings and modules
    • A.3. Regular sequences and Cohen–Macaulay algebras
    • A.4. Formality and Massey products
  • Appendix B. Algebraic Topology
    • B.1. Homotopy and homology
    • B.2. Elements of rational homotopy theory
    • B.3. Eilenberg–Moore spectral sequences
    • B.4. Group actions and equivariant topology
    • B.5. Stably complex structures
    • B.6. Weights and signs of torus actions
  • Appendix C. Categorical Constructions
    • C.1. Diagrams and model categories
    • C.2. Algebraic model categories
    • C.3. Homotopy limits and colimits
  • Appendix D. Bordism and Cobordism
    • D.1. Bordism of manifolds
    • D.2. Thom spaces and cobordism functors
    • D.3. Oriented and complex bordism
    • D.4. Characteristic classes and numbers
    • D.5. Structure results
    • D.6. Ring generators
  • Appendix E. Formal Group Laws and Hirzebruch Genera
    • E.1. Elements of the theory of formal group laws
    • E.2. Formal group law of geometric cobordisms
    • E.3. Hirzebruch genera (complex case)
    • E.4. Hirzebruch genera (oriented case)
    • E.5. Krichever genus
  • Bibliography
  • Index

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